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The numbers of blue, red, green and black pencils are proportional to the numbers 2, 3, 5, and 7, respectively. If we add the nu

Vitek1552 [10]

Answer:

20 green pencils

Step-by-step explanation:

The difference between black and green "ratio units" is 7 -5 = 2. The difference between red and blue ratio units is 3 -2 = 1. The sum of those differences is 2 +1 = 3 ratio units, which represent 12 pencils. Then each ratio unit represents 12/3 = 4 pencils.

The 5 ratio units of green pencils represent 5·4 pencils = 20 green pencils.

_____

If you need an equation, you can use k as the constant of proportionality. Then the sum of differences described is ...

(7k -5k) + (3k -2k) = 12

3k = 12 . . . . simplify

k = 4 . . . . . . divide by 3

5k = 5·4 = 20 . . . . . number of green pencils

6 0

3 years ago

Read 2 more answers

Translate the statement into an equation: the difference of four times a number and eight is equal to twenty-three less than tha

neonofarm [45]

Let, the number be "x"
Now,
according to the question,
4x -8 = x -23....................This is your equation.

Now solving it,
4x - 8 = x - 23
4x - x = -23 + 8
3x = -15
x = -15 / 3
x = -5

Checking the answer,
4 (-5) - 8 = (-5) - 23
-20 - 8 = -5 - 23
-28 = -28......................................true

6 0

3 years ago

Read 2 more answers

#19 please I’m literally failing math

ankoles [38]

Answer:

$51.12

Step-by-step explanation:

Hello there!

In number 19, we want to find the total price of a sweatshirt that costs $48 dollars but has 6.5% sales tax

Sales tax is a small percentage of the cost of an item that is added to items when they are being sold.

In this problem, 6.5% of the cost of the sweatshirt will be added to the cost of the sweatshirt in the form of sales tax. The price of the sweatshirt plus the amount in sales tax will be the total cost of the sweatshirt.

Translating that as an equation,

48 + 48*6.5%=total cost

You can calculate 48*6.5% as $\frac{48*6.5}{100}$ , which is equal to 3.12

So that means that $3.12 will be added to the cost of the sweatshirt.

Therefore,

48 + 3.12=$51.12, which will be the total cost of the sweatshirt, including sales tax

Hope this helps!

7 0

2 years ago

A woman bought some large frames for $18 each and some small frames for $8 each at a closeout sale. If she bought 21 frames fo

IrinaVladis [17]

Answer:

8 large frames and 13 small frames

Step-by-step explanation:

Given:
$18 each = large frames

$8 each = small frames

To Find:

⇒ Bought 21 frames for $248, find how many of each type she bought

Solve:

1 Large frame costs = 18 $

Therefore, x large frames costs = 18x $

{where x is the number of large frames she bought}

1 Small frame costs = 8 $

Therefore, x Small frames costs = 8y $

{where y is the number of small frames she bought}

By the given condition :

18x + 8y = 248 {equation 1}

x + y = 21 {equation 2}

Solve these equations simultaneously, from second equation we get :

x = 21- y

18⋅(21−y)+8y= 248

378 - 18y+8y = 248

-10y = -130

y = 13

Put y = 13 in eq x = 21- y

x = 21 - y

x = 21 - 13

x = 8

So the woman bought 8 large frames and 13 small frames.

~lenvy~

5 0

2 years ago

Function: y=3 sin(x) + 5

oksian1 [2.3K]

Answer:

see explanation

Step-by-step explanation:

The function has a maximum value when sinx = 1 , then

y = 3(1) + 5 = 3 + 5 = 8

The function has a minimum value when sinx = - 1, then

y = 3(- 1) + 5 = - 3 + 5 = 2

Thus

range is 2 < y < 8

6 0

2 years ago